Worksheet activity for identifying palindromes by circling numbers and performing addition and subtraction.

Problem Analysis:

The task involves identifying palindromes from a list of numbers and then finding the palindromes of the remaining numbers by repeatedly adding each number to its reverse until a palindrome is obtained. A palindrome is a number that reads the same backward as forward (e.g., 22, 55, 99).

Steps to Solve:

1. Identify Palindromes:
- A number is a palindrome if it reads the same backward as forward.
- Circle all such numbers in the given list.

2. Find Palindromes for Non-Palindromic Numbers:
- For each non-palindromic number, reverse it and add it to the original number.
- Check if the result is a palindrome. If not, repeat the process with the new sum until a palindrome is obtained.
- Write the resulting palindrome next to the original number.

Solution:

#### Step 1: Identify Palindromes
From the list of numbers (20 to 99), the palindromes are:
- 22, 33, 44, 55, 66, 77, 88, 99

Circle these numbers in the table.

#### Step 2: Find Palindromes for Non-Palindromic Numbers
We will now work through each non-palindromic number step by step.

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##### Example 1: Number 21
1. Reverse of 21 is 12.
2. Add: \( 21 + 12 = 33 \).
3. Check if 33 is a palindrome: Yes.
4. Result: 33

##### Example 2: Number 23
1. Reverse of 23 is 32.
2. Add: \( 23 + 32 = 55 \).
3. Check if 55 is a palindrome: Yes.
4. Result: 55

##### Example 3: Number 24
1. Reverse of 24 is 42.
2. Add: \( 24 + 42 = 66 \).
3. Check if 66 is a palindrome: Yes.
4. Result: 66

##### Example 4: Number 27
1. Reverse of 27 is 72.
2. Add: \( 27 + 72 = 99 \).
3. Check if 99 is a palindrome: Yes.
4. Result: 99

##### Example 5: Number 30
1. Reverse of 30 is 03 (or simply 3).
2. Add: \( 30 + 3 = 33 \).
3. Check if 33 is a palindrome: Yes.
4. Result: 33

##### Example 6: Number 31
1. Reverse of 31 is 13.
2. Add: \( 31 + 13 = 44 \).
3. Check if 44 is a palindrome: Yes.
4. Result: 44

##### Example 7: Number 32
1. Reverse of 32 is 23.
2. Add: \( 32 + 23 = 55 \).
3. Check if 55 is a palindrome: Yes.
4. Result: 55

##### Example 8: Number 34
1. Reverse of 34 is 43.
2. Add: \( 34 + 43 = 77 \).
3. Check if 77 is a palindrome: Yes.
4. Result: 77

##### Example 9: Number 35
1. Reverse of 35 is 53.
2. Add: \( 35 + 53 = 88 \).
3. Check if 88 is a palindrome: Yes.
4. Result: 88

##### Example 10: Number 36
1. Reverse of 36 is 63.
2. Add: \( 36 + 63 = 99 \).
3. Check if 99 is a palindrome: Yes.
4. Result: 99

##### Example 11: Number 37
1. Reverse of 37 is 73.
2. Add: \( 37 + 73 = 110 \).
3. Reverse of 110 is 011 (or 11).
4. Add: \( 110 + 11 = 121 \).
5. Check if 121 is a palindrome: Yes.
6. Result: 121

##### Example 12: Number 38
1. Reverse of 38 is 83.
2. Add: \( 38 + 83 = 121 \).
3. Check if 121 is a palindrome: Yes.
4. Result: 121

##### Example 13: Number 39
1. Reverse of 39 is 93.
2. Add: \( 39 + 93 = 132 \).
3. Reverse of 132 is 231.
4. Add: \( 132 + 231 = 363 \).
5. Check if 363 is a palindrome: Yes.
6. Result: 363

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Final Results:

Here is the completed table:

| Number | Palindromes |
|--------|-------------|
| 20 | 22 |
| 21 | 33 |
| 22 | 22 |
| 23 | 55 |
| 24 | 66 |
| 25 | 88 |
| 26 | 88 |
| 27 | 99 |
| 28 | 88 |
| 29 | 121 |
| 30 | 33 |
| 31 | 44 |
| 32 | 55 |
| 33 | 33 |
| 34 | 77 |
| 35 | 88 |
| 36 | 99 |
| 37 | 121 |
| 38 | 121 |
| 39 | 363 |

Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Number} & \text{Palindromes} \\
\hline
20 & 22 \\
21 & 33 \\
22 & 22 \\
23 & 55 \\
24 & 66 \\
25 & 88 \\
26 & 88 \\
27 & 99 \\
28 & 88 \\
29 & 121 \\
30 & 33 \\
31 & 44 \\
32 & 55 \\
33 & 33 \\
34 & 77 \\
35 & 88 \\
36 & 99 \\
37 & 121 \\
38 & 121 \\
39 & 363 \\
\end{array}
}
\]